Question
Find the slant asymptote x^2+7x-7/x-2
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Answered by
GPT 3.5
To find the slant asymptote of the rational function (x^2+7x-7)/(x-2), we need to divide the numerator (x^2+7x-7) by the denominator (x-2) using long division or synthetic division.
Using long division:
x + 9
___________________
x - 2 | x^2 + 7x - 7
- (x^2 - 2x)
__________
9x - 7
- (9x - 18)
___________
11
The quotient is x + 9, and the remainder is 11.
Therefore, the slant asymptote is given by the equation y = x + 9.
Note: The degrees of the numerator and denominator are the same (both are 1), so there is no horizontal asymptote. Instead, there is a slant asymptote.
Using long division:
x + 9
___________________
x - 2 | x^2 + 7x - 7
- (x^2 - 2x)
__________
9x - 7
- (9x - 18)
___________
11
The quotient is x + 9, and the remainder is 11.
Therefore, the slant asymptote is given by the equation y = x + 9.
Note: The degrees of the numerator and denominator are the same (both are 1), so there is no horizontal asymptote. Instead, there is a slant asymptote.
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